Utility functions which ensure the adequacy of stationary strategies

Monticino, Michael G.

doi:10.1090/S0002-9947-1991-0998355-1

Utility functions which ensure the adequacy of stationary strategies
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by Michael G. Monticino PDF

Trans. Amer. Math. Soc. 325 (1991), 187-204 Request permission

Abstract:

Within a Dubins and Savage gambling framework, a stationary strategy is a strategy which selects a gamble at each time based solely on the gambler’s present fortune. We determine conditions upon the gambler’s utility function under which stationary strategies allow the gambler to maximize his return. The class of utility functions which satisfies these conditions, termed nearly leavable shift invariant functions, is large and contains many of the common gambling utility functions. Moreover, this class is closed under uniform limits. These results are obtained with the setting of an analytic gambling house.

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